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Applied Mathematics and Mechanics

, Volume 38, Issue 1, pp 73–98 | Cite as

Mechanical and thermal postbuckling of FGM thick circular cylindrical shells reinforced by FGM stiffener system using higher-order shear deformation theory

  • D. V. Dung
  • H. T. ThiemEmail author
Article

Abstract

The postbuckling of the eccentrically stiffened circular cylindrical shells made of functionally graded materials (FGMs), subjected to the axial compressive load and external uniform pressure and filled inside by the elastic foundations in the thermal envi-ronments, is investigated with an analytical method. The shells are reinforced by FGM stringers and rings. The thermal elements of the shells and stiffeners in the fundamen-tal equations are considered. The equilibrium and nonlinear stability equations in terms of the displacement components for the stiffened shells are derived with the third-order shear deformation theory and Leckhniskii smeared stiffener technique. The closed-form expressions for determining the buckling load and postbuckling load-deflection curves are obtained with the Galerkin method. The effects of the stiffeners, the foundations, the material and dimensional parameters, and the pre-existent axial compressive and thermal load are considered.

Keywords

stiffened cylindrical shell functionally graded material (FGM) postbuckling elastic foundation analytical 

Chinese Library Classification

O344.3 

2010 Mathematics Subject Classification

74K25 74D05 74G60 

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References

  1. [1]
    Reddy, J. N. Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, CRC Press, Boca Raton (2004)zbMATHGoogle Scholar
  2. [2]
    Sheng, G. G. and Wang, X, Thermal vibration, buckling and dynamic stability of functionally graded cylindrical shells embedded in an elastic medium. Thermal vibration, buckling and dynamic stability of functionally graded cylindrical shells embedded in an elastic medium 27, 117–134 (2008)Google Scholar
  3. [3]
    Shen, H. S., Yang, J., and Kitipornchai, S, Postbuckling of internal pressure loaded FGM cylindri-cal shells surrounded by an elastic medium. Postbuckling of internal pressure loaded FGM cylindri-cal shells surrounded by an elastic medium 29, 448–460 (2010)Google Scholar
  4. [4]
    Sofiyev, A. N. and Avcar, M, The stability of cylindrical shells containing an FGM layer subjected to axial load on the Pasternak foundation. The stability of cylindrical shells containing an FGM layer subjected to axial load on the Pasternak foundation 2, 228–236 (2010)Google Scholar
  5. [5]
    Sofiyev, A. N, Buckling analysis of FGM circular shells under combined loads and resting on the Pasternak type elastic foundation. Buckling analysis of FGM circular shells under combined loads and resting on the Pasternak type elastic foundation 37, 539–544 (2010)zbMATHGoogle Scholar
  6. [6]
    Sofiyev, A. H. and Kuruoglu, N, Torsional vibration and buckling of the cylindrical shell with functionally graded coatings surrounded by an elastic medium. Torsional vibration and buckling of the cylindrical shell with functionally graded coatings surrounded by an elastic medium 45, 1133–1142 (2013)Google Scholar
  7. [7]
    Bagherizadeh, E., Kiani, Y., and Eslami, M. R, Mechanical buckling of functionally graded ma-terial cylindrical shells surrounded by Pasternak elastic foundation. Mechanical buckling of functionally graded ma-terial cylindrical shells surrounded by Pasternak elastic foundation 93, 3063–3071 (2011)Google Scholar
  8. [8]
    Shen, H. S, Postbuckling analysis of pressure-loaded functionally graded cylindrical shells in ther-mal environments. Postbuckling analysis of pressure-loaded functionally graded cylindrical shells in ther-mal environments 25, 487–497 (2003)Google Scholar
  9. [9]
    Huang, H. and Han, Q, Nonlinear dynamic buckling of functionally graded cylindrical shells subjected to time dependent axial load. Nonlinear dynamic buckling of functionally graded cylindrical shells subjected to time dependent axial load 92, 593–598 (2010)Google Scholar
  10. [10]
    Bahadori, R. and Najafizadeh, M. M, Free vibration analysis of two-dimensional functionally graded axisymmetric cylindrical shell on Winkler-Pasternak elastic foundation by first-order shear deformation theory and using Navier-differential quadrature solution methods. Free vibration analysis of two-dimensional functionally graded axisymmetric cylindrical shell on Winkler-Pasternak elastic foundation by first-order shear deformation theory and using Navier-differential quadrature solution methods 39, 4877–4894 (2015)MathSciNetGoogle Scholar
  11. [11]
    Li, Z. M. and Qiao, P, Buckling and postbuckling of anisotropic laminated cylindrical shells under combined external pressure and axial compression in thermal environments. Buckling and postbuckling of anisotropic laminated cylindrical shells under combined external pressure and axial compression in thermal environments 119, 709–726 (2015)Google Scholar
  12. [12]
    Shen, H. S. and Wang, H, Nonlinear bending and postbuckling of FGM cylindrical panels subjected to combined loadings and resting on elastic foundations in thermal environments. Nonlinear bending and postbuckling of FGM cylindrical panels subjected to combined loadings and resting on elastic foundations in thermal environments 78, 202–213 (2015)Google Scholar
  13. [13]
    Sofiyev, A. H, Influences of shear stresses on the dynamic instability of exponentially graded sandwich cylindrical shells. Influences of shear stresses on the dynamic instability of exponentially graded sandwich cylindrical shells 77, 349–362 (2015)Google Scholar
  14. [14]
    Sofiyev, A. H, Buckling of heterogeneous orthotropic composite conical shells under external pressures within the shear deformation theory. Buckling of heterogeneous orthotropic composite conical shells under external pressures within the shear deformation theory 84, 175–187 (2016)Google Scholar
  15. [15]
    Sofiyev, A. H, Thermoelastic stability of freely supported functionally graded conical shells within the shear deformation theory. Thermoelastic stability of freely supported functionally graded conical shells within the shear deformation theory 152, 74–84 (2016)Google Scholar
  16. [16]
    Baruch, M. and Singer, J, Effect of eccentricity of stiffeners on the general instability of stiffened cylindrical shells under hydro-static pressure. Effect of eccentricity of stiffeners on the general instability of stiffened cylindrical shells under hydro-static pressure 5, 23–27 (1963)Google Scholar
  17. [17]
    Ji, Z. Y. and Yeh, K. Y, General solution for nonlinear buckling of non-homogeneous axial sym-metric ring-and stringer-stiffened cylindrical shells. General solution for nonlinear buckling of non-homogeneous axial sym-metric ring-and stringer-stiffened cylindrical shells 34, 585–591 (1990)zbMATHGoogle Scholar
  18. [18]
    Reddy, J. N. and Starnes, J. H, General buckling of stiffened circular cylindrical shells according to a Layerwise theory. General buckling of stiffened circular cylindrical shells according to a Layerwise theory 49, 605–616 (1993)zbMATHGoogle Scholar
  19. [19]
    Shen, H. S., Zhou, P., and Chen, T. Y, Postbuckling analysis of stiffened cylindrical shells under combined external pressure and axial compression. Postbuckling analysis of stiffened cylindrical shells under combined external pressure and axial compression 15, 43–63 (1993)Google Scholar
  20. [20]
    Tian, J., Wang, C. M., and Swaddiwudhipong, S, Elastic buckling analysis of ring-stiffened cylin-drical shells under general pressure loading via the Ritz method. Elastic buckling analysis of ring-stiffened cylin-drical shells under general pressure loading via the Ritz method 35, 1–24 (1999)Google Scholar
  21. [21]
    Sadeghifar, M., Bagheri, M., and Jafari, A. A, Buckling analysis of stringer-stiffened laminated cylindrical shells with non-uniform eccentricity. Buckling analysis of stringer-stiffened laminated cylindrical shells with non-uniform eccentricity 81, 875–886 (2011)zbMATHGoogle Scholar
  22. [22]
    Stamatelos, D. G., Labeas, G. N, and Tserpes, K. I, Analytical calculation of local buckling and postbuckling behavior of isotropic and orthotropic stiffened panels. Analytical calculation of local buckling and postbuckling behavior of isotropic and orthotropic stiffened panels 49, 422–430 (2011)Google Scholar
  23. [23]
    Bich, D. H., Dung, D. V., and Nam, V. H, Nonlinear dynamic analysis of eccentrically stiffened imperfect functionally graded doubly curved thin shallow shells. Nonlinear dynamic analysis of eccentrically stiffened imperfect functionally graded doubly curved thin shallow shells 96, 384–395 (2013)Google Scholar
  24. [24]
    Bich, D. H., Dung, D. V., Nam, V. H., and Phuong, N. T, Nonlinear static and dynamical buckling analysis of imperfect eccentrically stiffened functionally graded circular cylindrical thin shells under axial compression. Nonlinear static and dynamical buckling analysis of imperfect eccentrically stiffened functionally graded circular cylindrical thin shells under axial compression 74, 190–200 (2013)Google Scholar
  25. [25]
    Dung, D. V. and Nam, V. H, Nonlinear dynamic analysis of eccentrically stiffened function-ally graded circular cylindrical thin shells under external pressure and surrounded by an elastic medium. Nonlinear dynamic analysis of eccentrically stiffened function-ally graded circular cylindrical thin shells under external pressure and surrounded by an elastic medium 46, 42–53 (2014)Google Scholar
  26. [26]
    Duc, N. D. and Quan, T. Q, Nonlinear dynamic analysis of imperfect FGM double curved thin shallow shells with temperature-dependent properties on elastic foundation. Nonlinear dynamic analysis of imperfect FGM double curved thin shallow shells with temperature-dependent properties on elastic foundation 21, 1340–1362 (2015)Google Scholar
  27. [27]
    Najafizadeh, M. M., Hasani, A., and Khazaeinejad, P, Mechanical stability of functionally graded stiffened cylindrical shells. Mechanical stability of functionally graded stiffened cylindrical shells 33, 1151–1157 (2009)MathSciNetzbMATHGoogle Scholar
  28. [28]
    Dung, D. V. and Hoa, L. K, Nonlinear torsional buckling and postbuckling of eccentrically stiffened FGM cylindrical shells in thermal environment. Nonlinear torsional buckling and postbuckling of eccentrically stiffened FGM cylindrical shells in thermal environment 69, 378–388 (2015)Google Scholar
  29. [29]
    Dung, D. V. and Hoa, L. K, Semi-analytical approach for analyzing the nonlinear dynamic tor-sional buckling of stiffened functionally graded material circular cylindrical shells surrounded by an elastic medium. Semi-analytical approach for analyzing the nonlinear dynamic tor-sional buckling of stiffened functionally graded material circular cylindrical shells surrounded by an elastic medium 39, 6951–6967 (2015)Google Scholar
  30. [30]
    Brush, D. D. and Almroth, B. O. Buckling of Bars, Plates and Shells, McGraw-Hill, New York (1975)zbMATHGoogle Scholar

Copyright information

© Shanghai University and Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Faculty of Mathematics, Mechanics and InformaticsVietnam National UniversityHanoiVietnam

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